Will running an LED designed for batteries on a NEXUS dynamo hub damage the LED?

6v is probably low enough to not damage the LED, but you might be vulnerable to a voltage spike. You could use a regular diode in series to help protect the headlight.

Reverse pulses at low voltage probably won't damage the LED, but the COB (chip on board) that gives the flashing modes might not be able to cope with the full reverse voltage.

The problem is that the hub dynamo is more accurately a constant current source, and will supply about 500mA. One common trick is to run two 6V lights in series off a hub dynamo, and most dynamos will give full brightness from both... they put out 12V. The actual voltage you get out of it might be clamped by a zener, but it's unlikely to be a 5W zener that can take the full power of the hub forever. Not that you want that anyway, it's extra drag.

I have run bare 5W star LEDs straight off a SON hub dynamo (well, with a diode and capacitor to reduce flickering) because they're designed to take 500mA and that's what the dynamo supplies. It worked really well, just using a chunk of aluminium channel as a heat sink/weather sheild/reflector. I don't really know about longevity, after ~10,000km/a year or so I got a proper light cheap so switched to that.

So if your 6V LED is actually a 1W light it might be getting 12V or more. Whether it survives that is anyone's guess. Worse, even a 5W light is likely to be getting +6V on that half of the wave, then -12V on the other half when it's not drawing any power. I suggest a basic diode or bridge rectifier in series, capacitor in parallel to give you DC.

I think the best solution is to get a light built for that particular hub. That way I can be sure that it's engineered to work properly with that system. It's a shame--that light looks so good with this bike. .

LEDs don't like negative voltages. They generally fry at some 3x-5x their normal forward voltage.

Then again, you don't have a bare LED, but a LED and a LED controller and it is the controller that is likely to suffer first. The bad thing is, we don't know much about it.

Another bad thing is that the 6v hub is actually 6v when properly loaded w/ 6V, 3W bulb. Otherwise it can go very high, like 50V.

You'll get prettu much extra complexity if you try to do the proper thing.

You can as well opt for a simple & stupid solution like hub => bridge rectifier => 1.5W white led (bare, without controller). It will behave almost like a bulb, except for the brighter light and about half the drag.